There's a book I have I bought I think on Ebay called Treatise On the Accompaniment of Gregorian Chant by Henri Potiron, trans. by Ruth C. Gabain. It says on the cover Potironm (since I didn't know who he was) was choir master at Sacre-Coeur and prof. at the Greogian Institute. Check ebay and check www.bookfinder.com which lets you search all the used booksites at once.

The best I've seen (and I have it only in photo-copy form) is by Flor Peeters. His style is strictly modal, i.e. not just major/minor chords superimposed on the melody. It is very detailed with many examples of both do's and don't's.

Other English language instruction books on Gregorian Chant accompaniment include the following according to the Library of Congress (loc.gov) catalog:

LC Control No.: 28012049
LCCN Permalink: http://lccn.loc.gov/28012049
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Arnold, J. H. (John Henry), 1887-1956.
Main Title: Plainsong accompaniment, by J. H. Arnold; with a preface by Geoffrey Shaw.
Published/Created: London, Oxford university press, H. Milford [1927]
Description: xv, 175 p. illus. (music) 26 cm.
Notes: "Examples": p. [105]-143.
"Tone table and harmonies": p. [145]-170.
Subjects: Gregorian chants --Accompaniments --Instruction and study.
LC Classification: MT190 .A2
Other System No.: (OCoLC)958729

LC Control No.: unk84114781
LCCN Permalink: http://lccn.loc.gov/unk84114781
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Cecile, Sister. [from old catalog]
Main Title: Chant accompaniment simplified.
Published/Created: [Collegeville, Minn., Liturgical Press, 1960]
Description: 15 p. cm.
Subjects: Gregorian chants --Accompaniments --Instruction and study.
LC Classification: MT190 .C4

LC Control No.: 64055831
LCCN Permalink: http://lccn.loc.gov/64055831
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Fleming, Michael P. M.
Main Title: The accompaniment of plainsong.
Published/Created: Croydon [Eng.] Royal School of Church Music [1963?]
Description: 16 p. music 22 cm.
Notes: Bibliography: p. 16.
Subjects: Gregorian chants --Accompaniments --Instruction and study.
Series: Royal School of Church Music. Study notes, no. 11
LC Classification: MT190 .F6

LC Control No.: 50026376
LCCN Permalink: http://lccn.loc.gov/50026376
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Lapierre, Eugène, 1899-1970.
Main Title: Gregorian chant accompaniment. A new and simple approach according to the theory of the basic modal intervals.
Edition Information: [1st ed.]
Published/Created: Toledo, Gregorian Institute of America [1949]
Description: 103 p. music. 25 cm.
Subjects: Gregorian chants --Accompaniments --Instruction and study.
LC Classification: MT190 .L3
Other System No.: (OCoLC)1016223

LC Control No.: 50056132
LCCN Permalink: http://lccn.loc.gov/50056132
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Peeters, Flor, 1903-1986.
Uniform Title: Méthode pratique pour l’accompagnement du chant grégorien
Main Title: Méthode pratique pour l’accompagnement du chant grégorien. A practical method of plain-chant accompaniment.
Published/Created: Malines, H. Dessain [1949].
Related Titles: Practical method of plain-chant accompaniment.
Description: vii, 99 p. 33 cm.
Notes: French and English text.
Bibliography: p. 97. "Catalogue of the published works of Flor Peeters": p. 98-99.
Subjects: Gregorian chants --Accompaniments --Instruction and study.
LC Classification: MT190 .P4 1949
Language Code: engfre
Other System No.: (OCoLC)2215968

LC Control No.: 08031853
LCCN Permalink: http://lccn.loc.gov/08031853
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Springer, Max, 1877-
Main Title: The art of accompanying plain chant, by Max Springer...translated from the German by the Benedictine fathers, Conception, Mo., U.S.A.
Published/Created: New York, J. Fischer & bro., 1908.
Description: xiii,238 p. music 23 cm.
Notes: Includes index.
Subjects: Gregorian chants --Accompaniments --Instruction and study.
Series: Fischers edition no. 3050
LC Classification: MT190 .S67
Other System No.: (OCoLC)3026311

LC Control No.: 59014352
LCCN Permalink: http://lccn.loc.gov/59014352
Type of Material: Book (Print, Microform, Electronic, etc.)
Personal Name: Weakland, Rembert.
Main Title: Modal acccompaniment.
Published/Created: Latrobe, Pa., Archabbey Press, 1959.
Description: v, 82 l. music. 29 cm.
Notes: Selections from the Liber usualis (Gregorian notation) : leaves 78-82.
Subjects: Gregorian chants --Accompaniments --Instruction and study.
LC Classification: MT190 .W4
Dewey Class No.: 783.5
Other System No.: (OCoLC)6445947

Thank you.

John D. Horton
Tacoma, Washington
USA